Properties of galaxy dark matter halos from weak lensing
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借助引力探测暗物质
邓雪梅
【期刊名称】《世界科学》
【年(卷),期】2008(000)004
【摘要】爱因斯坦曾预言:诸如星系的大质量天体的引力犹如透镜一样会使光线
弯曲。
从某种意义上说,这样的星系“透镜”能对应于星系以外的远距离天体成像。
为此,天文学家花费了几十年的时间来研究引力透镜,现在他们准备把这些引力透镜作为工具来检验宇宙结构和演化的最新理论。
【总页数】1页(P3)
【作者】邓雪梅
【作者单位】无
【正文语种】中文
【中图分类】P159
【相关文献】
1.引力透镜效应与暗物质探测 [J], 苏宜
2.基于F-W暗物质模型的暗物质探测仪的设计思路 [J], 陈紫微
3.LIGO真的探测到引力波了吗?——电磁相互作用的存在导致LIGO探测引力波的实验无效 [J], 梅晓春;俞平
4.暗物质的发现及其粒子探测——记中国科学院暗物质与空间天文重点实验室 [J], 袁强;范一中;常进;
5.面向暗物质直接探测的原型液氩探测器读出电子学系统设计 [J], 祝星;沈仲弢;赵珂庆;熊卫星;于翰霖;封常青;刘树彬;安琪
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从万有引力出发对黑洞、暗物质和暗能量的分析与理解
陈小波
【期刊名称】《重庆文理学院学报(自然科学版)》
【年(卷),期】2010(029)001
【摘要】万有引力具有两个基本特性:普适性和纯粹吸引作用,重力系统的能量则必须是正定的.从万有引力出发,在牛顿力学的基础上进行简单推导得到了一些关系式,对黑洞、暗物质和暗能量等一些物理课题进行一定程度的分析和理解.
【总页数】3页(P53-55)
【作者】陈小波
【作者单位】四川文理学院,物理与工程技术系,四川,达州,635000
【正文语种】中文
【中图分类】O314
【相关文献】
1.从万有引力出发对黑洞、暗物质和暗能量的分析与理解 [J], 陈小波;
2.阴阳说:从宇宙暗物质的发现到生命暗物质和暗能量的研究 [J], 冯前进
3.哈勃定律的证明与宇宙膨胀的真相及暗物质和暗能量 [J], 钟萃相
4.哈勃定律的证明与宇宙膨胀的真相及暗物质和暗能量 [J], 钟萃相
5.对暗物质和暗能量的全新解读 [J], 章洛汗;张诗晗
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黑洞四定律黑洞四定律是关于黑洞性质及行为的重要定律,对于理解黑洞的基本性质和其与物理学的关系具有重要意义。
黑洞四定律包括黑洞的质量、面积、角动量和电荷四个方面。
下面将逐一介绍这些定律,并提供一些相关参考内容。
1. 黑洞质量定律:黑洞质量定律,也被称为霍金面积定律,它指出黑洞的表面积和质量之间存在着一种关系,即黑洞的表面积正比于其质量的平方。
这个定律是由物理学家斯蒂芬·霍金于1971年提出的。
霍金面积定律是黑洞热力学理论的基础,它将黑洞与热力学的概念进行了联系,使人们能够通过研究黑洞的热力学性质来更好地理解黑洞。
参考内容:- 斯蒂芬·霍金, "Black Hole Explosions?" Nature, vol. 248, pp. 30-31, 1974.- Andrei Barvinsky, George Kunstatter, "Critical Phenomena in Black Hole Physics," Phys. Lett. B, vol. 389, no. 3-4, pp. 231-236, 1996.- 黄绪淇, "黑洞的热力学与量子论," 物理学报, vol. 52, no. 7, pp. 1359-1366, 2003.2. 黑洞面积定律:根据黑洞的面积定律,也称为麦克斯韦-比克尔定律,黑洞的面积与其事件视界的面积成正比。
黑洞的事件视界是黑洞的边界,当物质趋于接近黑洞时,一旦穿过该边界,就无法再逃脱黑洞的引力。
参考内容:- 麦克斯韦, "On the Dynamical Theory of Gases," Proceedings of the Royal Society of Edinburgh, vol. 2, pp. 1-21, 1867.- J. D. Bekenstein, "Black Holes and Entropy," Physical Review D, vol. 7, no. 8, pp. 2333-2346, 1973.- 斯蒂芬·霍金, "Particle Creation by Black Holes," Communications in Mathematical Physics, vol. 43, no. 3, pp. 199-220, 1975.3. 黑洞角动量定律:黑洞角动量定律是根据黑洞旋转的性质推导出来的定律。
AXIONSGEORG RAFFELTMax-Planck-Institut für Physik(Werner-Heisenberg-Institut),Föhringer Ring6,80805München,Germany(e-mail:*****************.de)(Received7August2001;accepted29August2001)Abstract.Axions are one of the few particle-physics candidates for dark matter which are well motivated independently of their possible cosmological role.A brief review is given of the theoreticalmotivation for axions,their possible role in cosmology,the existing astrophysical limits,and thestatus of experimental searches.1.IntroductionDespite its uncanny success,the particle-physics standard model has many looseends,among them the CP problem of quantum chromodynamics(QCD).The non-trivialfield structure of the QCD ground state(‘ -vacuum’)and a phase of thequark mass matrix each induce a non-perturbative CP-violating term in the QCDLagrangian which is proportional to the coefficient = QCD+arg det M quark, where could lie anywhere between0and2π.The experimental upper limit to aputative neutron electric dipole moment,a CP-violating quantity,informs us that 10−9,a severefine-tuning problem given that is a sum of two unrelated terms which would be expected to be of order unity each.One particularly elegant solution was proposed by Peccei and Quinn,where theparameter is re-interpreted as a dynamical variable, →a(x)/f a,where a(x)isthe axionfield and f a an energy scale called the Peccei-Quinn scale or axion decayconstant(Peccei and Quinn,1977a,b;Weinberg,1977;Wilczek,1977).The previ-ous CP-violating term automatically includes a potential for the axionfield whichdrives it to its CP-conserving minimum(dynamical symmetry restoration).Whilethis may sound complicated,Sikivie(1996)has constructed a beautiful mechanicalanalogy which nicely explains the main features of axion physics.While axions would be very weakly interacting,they are still a QCD phenom-enon.They share their quantum numbers with neutral pions;all generic axionproperties are roughly determined by those ofπ0,scaled with fπ/f a where fπ= 93MeV is the pion decay constant.For example,the axion mass is roughly given by m a f a=mπfπ,and the coupling to photons or nucleons is roughly suppressed by fπ/f a relative to the pion couplings.Axions have not been found during the quarter century since they werefirstproposed,but the interest in this hypothesis is well alive because other proposed Space Science Reviews100:153–158,2002.©2002Kluwer Academic Publishers.Printed in the Netherlands.154G.RAFFELTsolutions of the strong CP problem are not clearly superior,and mainly because axions are one of the few well-motivated particle candidates for the cold dark matter which apparently dominates the dynamics of the universe.The current status of axions physics and astrophysics was reviewed at a recent conference(Sikivie,1999).Particle-physics aspects,the status of astrophysical limits,and that of current search experiments are summarized in three separate mini-reviews in the Review of Particle Physics(Groom et al.,2000).Chapters on axions are also found in some textbooks(Kolb and Turner,1990;Raffelt,1996).For theoretical reviews see Kim(1987)and Cheng(1988),for a review of experimental searches see Rosenberg and van Bibber(2000).2.Stellar-Evolution LimitsThe main argument which proves that the Peccei-Quinn scale f a must be very large, corresponding to a very small axion mass m a,is related to stellar evolution.Axions would be produced by various processes in the hot and dense interior of stars and would thus carry away energy directly,much in analogy to the standard thermal neutrino losses.The strength of the axion interaction with photons,electrons,and nucleons can be constrained from the requirement that stellar-evolution time scales are not modified beyond observational limits(Raffelt,1996).For example,the helium-burning lifetime of horizontal-branch stars inferred from number counts in globular clusters reveals that the Primakoff processγ+Ze→Ze+a must not be too efficient in these stars,leading to a limit of m a 0.4eV(Figure1).Very restrictive limits arise from the observed neutrino signal of the supernova (SN)1987A.After collapse,the SN core is so hot and dense that neutrinos are trapped and escape only by diffusion so that it takes several seconds to cool a roughly solar-mass object the size of a few ten kilometers.The emission of axions would remove energy from the deep inner core which should show up in late-time neutrinos.Therefore,the observed duration of the SN1987A neutrino signal provides the most restrictive limits on the axion-nucleon coupling(Figure1).In the early papers on this topic,the difficulty of calculating the axion emission from a dense and hot nuclear medium had been underestimated;the most recent discussions attempt an inclusion of dense-medium effects(Janka et al.,1996).If axions are too‘strongly’interacting,they are trapped in a SN core,inval-idating the energy-loss argument and implying a mass above which axions are not excluded by the SN1987A signal(Turner,1988;Burrows et al.,1990).They would still carry away some of the energy and would cause excess counts in the water Cherenkov detectors which registered the neutrinos,allowing one to exclude another interval of axion masses(Engel et al.,1990).Probably there is a small crack of allowed axion masses between these two SN1987A arguments(Figure1), sometimes called the‘hadronic axion window’.Therefore,infine-tuned axion models where the tree-level coupling to photons nearly vanishes,eV-mass axionsAXIONS155Figure1.Astrophysical and cosmological exclusion regions(hatched)for the axion mass m a or the Peccei–Quinn scale f a.An‘open end’of an exclusion bar means that it represents a rough estimate. The globular cluster limit depends on the axion-photon coupling;it was assumed that E/N=83as in GUT models or the DFSZ model.The SN1987A limits depend on the axion-nucleon couplings; the shown case corresponds to the KSVZ model and approximately to the DFSZ model.The dot-ted‘inclusion regions’indicate where axions could plausibly be the cosmic dark matter.Most of the allowed range in the inflation scenario requiresfine-tuned initial conditions.Also shown is the projected sensitivity range of the search experiments for galactic dark-matter axions.may be allowed and could thus play the role of a cosmological hot dark matter component(Moroi and Murayama,1998).The axion coupling to electrons can be constrained from the properties of glob-ular-cluster stars and the white-dwarf luminosity function.However,the tree-level existence of such a coupling is not generic,and the resulting limits on m a and f a do not extend the range covered by the previous arguments.3.CosmologyIn the early universe,axions come into thermal equilibrium only if f a 108GeV, a region excluded by the stellar-evolution limits.For f a 108GeV cosmic axions are produced nonthermally.If inflation occurred after the Peccei-Quinn symmetry breaking or if T reheat<f a,the‘misalignment mechanism’(Preskill et al.,1983; Abbott and Sikivie,1983;Dine and Fischler,1983;Turner,1986)leads to a contri-bution to the cosmic critical density of a h2≈1.9×3±1(1µeV/m a)1.175 2i F( i)156G.RAFFELTwhere h is the Hubble constant in units of100km s−1Mpc−1.The stated range re-flects recognized uncertainties of the cosmic conditions at the QCD phase transition and of the temperature-dependent axion mass.The function F( )with F(0)=1 and F(π)=∞accounts for anharmonic corrections to the axion potential.Be-cause the initial misalignment angle i can be very small or very close toπ,there is no real prediction for the mass of dark-matter axions even though one wouldexpect 2i F( i)∼1to avoidfine-tuning the initial conditions.A possiblefine-tuning of i is limited by inflation-induced quantumfluctu-ations which in turn lead to temperaturefluctuations of the cosmic microwave background(Lyth,1990;Turner and Wilczek,1991;Linde,1991).In a broad class of inflationary models one thusfinds an upper limit to m a where axions could be the dark matter.According to the most recent discussion(Shellard and Battye,1998) it is about10−3eV(Figure1).If inflation did not occur at all or if it occurred before the Peccei-Quinn symme-try breaking with T reheat>f a,cosmic axion strings form by the Kibble mechanism (Davis,1986).Their motion is damped primarily by axion emission rather than gravitational waves.After axions acquire a mass at the QCD phase transition they quickly become nonrelativistic and thus form a cold dark matter component.The axion density is similar to that from the misalignment mechanism,but in detail the calculations are difficult and somewhat controversial between one group of authors(Davis,1986;Davis and Shellard,1989;Battye and Shellard,1994a,b)and another(Harari and Sikivie,1987;Hagmann and Sikivie,1991;Hagmann et al., 2001).Taking into account the uncertainty in various cosmological parameters one arrives at a plausible range for dark-matter axions as indicated in Figure1.4.Experimental SearchIf axions are indeed the dark matter of our galaxy one can search for them by the ‘haloscope’method(Sikivie,1983).The generic two-photon vertex which axions posess in analogy to neutral pions allows for the Primakoff conversion a↔γin the presence of external electromagneticfields.Therefore,the galactic axions should excite a microwave resonator which is placed in a strong magneticfield, i.e.,one expects a narrow line above the thermal noise of the cavity.While this line would not be difficult to identify once it has been found,searching for it requires to step a tunable cavity through many resonance intervals in order to cover a given m a range.In the late1980s,this method was pioneered in two pilot experiments (Wuensch et al.,1989;Hagmann et al.,1990).At the present time two full-scale ‘second generation’axion haloscopes are in operation,one in Livermore,Califor-nia(Hagmann et al.,1998,2000)and one in Kyoto,Japan(Ogawa et al.,1996; Yamamoto et al.,2001),the latter one using a beam of Rydberg atoms as a low-noise microwave detector.The projected sensitivity shown in Figure1covers the lower end of the plausible mass range for dark-matter axions.If axions are indeedAXIONS157 the galactic dark matter,these experiments for thefirst time are in a position to actually detect them.Axions or axion-like particles are currently also searched by the‘helioscope’method(Sikivie,1983;van Bibber et al.,1989).Axions would be produced in the Sun by the Primakoff effect,and could be back-converted into X-rays in a long dipole magnet oriented toward the Sun.A dedicated experiment of this sort in Tokyo has recently reported new limits(Inoue et al.,2000)while a much larger ef-fort using a decommissioned LHC test magnet,the CAST experiment,is currently under construction at CERN(Zioutas et al.,1999).It should be noted,however, that these searches are unrelated to axion dark matter,i.e.,if axions were to show up at CAST they almost certainly could not provide the cosmic dark matter.The evidence for the reality of dark matter has mounted for several decades,and most recently culminated with the determination of the cosmological parameters by cosmic-microwave precision experiments and other arguments.On the other hand, the physical nature of dark matter remains as mysterious as it was two decades ago. Therefore,the direct search experiments for particle candidates such as axions are among the most important efforts in the area of experimental cosmology.AcknowledgementsThis research was supported,in part,by the Deutsche Forschungsgemeinschaft under grant No.SFB-375and by the ESF network Neutrino Astrophysics.ReferencesAbbott,L.and Sikivie,P.:1983,‘A Cosmological Bound on the Invisible Axion’.Phys.Lett.B120, 133–136.Battye,R.A.and Shellard,E.P.S.:1994a,‘Global String Radiation’.Nucl.Phys.B423,260–304. Battye,R.A.and Shellard,E.P.S.:1994b,‘Axion String Constraints’.Phys.Rev.Lett.73,2954–2957;(E)ibid.76,2203–2204(1996).Burrows,A.,Ressel,T.and Turner,M.:1990,‘Axions and SN1987A:Axion trapping’.Phys.Rev.D42,3297–3309.Cheng,H.-Y.:1988,‘The Strong CP Problem Revisited’.Phys.Rept.158,1–89.Davis,R.L.:1986,‘Cosmic Axions from Cosmic Strings’.Phys.Lett.B180,225–230.Davis,R.L.and Shellard,E.P.S.:1989,‘Do Axions Need Inflation?’.Nucl.Phys.B324,167–186. Dine,M.and Fischler,W.:1983,‘The Not So Harmless Axion’.Phys.Lett.B120,137–141. Engel,J.,Seckel,D.and Hayes,A.C.:1990,‘Emission and Detectability of Hadronic Axions from SN1987A’.Phys.Rev.Lett.65,960–963.Groom,D.E.et al.:2000,‘The Review of Particle Physics’.Eur.Phys.J.C15,1–878.See also /Hagmann,C.and Sikivie,P.:1991,‘Computer Simulation of the Motion and Decay of Global Strings’.Nucl.Phys.B363,247–280.Hagmann,C.,Chang,S.and Sikivie,P.:2001,‘Axion Radiation from Strings’.Phys.Rev.D63, 125018(12pp).158G.RAFFELTHagmann,C.et al.:1990,‘Results from a Search for Cosmic Axions’.Phys.Rev.D42,1297–1300. Hagmann,C.et al.:1998,‘Results from a High-Sensitivity Search for Cosmic Axions’.Phys.Rev.Lett.80,2043–2046.Hagmann,C.et al.:2000,‘Cryogenic Cavity Detector for a Large-Scale Cold Dark-Matter Axion Search’.Nucl.Instrum.Meth.A444,569–583.Harari,D.and Sikivie,P.:1987,‘On the Evolution of Global Strings in the Early Universe’.Phys.Lett.B195,361–365.Inoue,Y.et al.:2000,‘Recent Results from the Tokyo Axion Helioscope Experiment’.astro-ph/0012338.Janka,H.-T.,Keil,W.,Raffelt,G.and Seckel,D.:1996,‘Nucleon Spin Fluctuations and the Supernova Emission of Neutrinos and Axions’.Phys.Rev.Lett.76,2621–2624.Kim,J.E.:1987.‘Light Pseudoscalars,Particle Physics and Cosmology’.Phys.Rept.150,1–177. Kolb,E.W.and Turner,M.S.:1990,‘The Early Universe’.Addison-Wesley,Reading,Mass. Linde,A.:1991,‘Axions in Inflationary Cosmology’.Phys.Lett.B259,38–47.Lyth,D.H.:1990,‘A Limit on the Inflationary Energy Density from Axion Isocurvature Fluctua-tions’.Phys.Lett.B236,408–410.Moroi,M.and Murayama,H.:1998,‘Axionic Hot Dark Matter in the Hadronic Axion Window’.Phys.Lett.B440,69–76.Ogawa,I.,Matsuki,S.and Yamamoto,K.:1996,‘Interactions of Cosmic Axions with Rydberg Atoms in Resonant Cavities Via the Primakoff Process’.Phys.Rev.D53,R1740–R1744. Peccei,R.D.and Quinn,H.R.:1977a,‘CP Conservation in the Presence of Instantons’.Phys.Rev.Lett.38,1440–1443.Peccei,R.D.and Quinn,H.R.:1977b,‘Constraints Imposed by CP Conservation in the Presence of Instantons’.Phys.Rev.D16,1791–1797.Preskill,J.,Wise,M.and Wilczek,F.:1983,‘Cosmology of the Invisible Axion’.Phys.Lett.B120, 127–132.Raffelt,G.G.:1996,‘Stars as Laboratories for Fundamental Physics’.University of Chicago Press. Rosenberg,L.and van Bibber,K.:2000,‘Searches for Invisible Axions’.Phys.Rept.325,1–39. Sikivie,P.:1983,‘Experimental Tests of the“Invisible”Axion’.Phys.Rev.Lett.51,1415–1417;(E) ibid.52,695(1984).Sikivie,P.:1996,‘The Pool Table Analogy to Axion Physics’.Physics Today49,22–27. Sikivie,P.(ed.):1999,‘Proceedings Axion Workshop’.Nucl.Phys.B(Proc.Suppl.)72,1–238. Shellard,E.P.S.and Battye,R.A.:1998,‘Cosmic Axions’.astro-ph/9802216.Turner,M.S.:1986,‘Cosmic and Local Mass Density of“Invisible”Axions’.Phys.Rev.D33,889–896.Turner,M.S.:1988,‘Axions from SN1987A’.Phys.Rev.Lett.60,1797–1800.Turner,M.S.and Wilczek,F.:1991,‘Inflationary Axion Cosmology’.Phys.Rev.Lett.66,5–8.van Bibber,K.et al.:1989,‘Design for a Practical Laboratory Detector for Solar Axions’.Phys.Rev.D39,2089–2099.Weinberg,S.:1978,‘A New Light Boson?’.Phys.Rev.Lett.40,223–226.Wilczek,F.:1978,‘Problem of Strong P and T Invariance in the Presence of Instantons’.Phys.Rev.Lett.40,279–282.Wuensch,W.U.et al.:1989,‘Results of a Laboratory Search for Cosmic Axions and Other Weakly Coupled Light Particles’.Phys.Rev.D40,3153–3167.Yamamoto,K.et al.:2001,‘The Rydberg Atom Cavity Axion Search’.hep-ph/0101200. Zioutas,K.et al.:1999,‘A Decommissioned LHC Model Magnet as an Axion Telescope’.Nucl.Instrum.Meth.A425,482–489.See also http://axnd02.cern.ch/CAST/。
do i:10.3969/j.issn0253 9608.2010.04.009引力透镜效应与暗物质探测*苏 宜教授,南开大学,天津300071*国家级教学团队建设项目 科学素质教育系列公共课教学团队 (教高函[2007]23号)关键词 引力透镜 暗物质 大爆炸 黑暗年代 爱因斯坦环引力透镜是广义相对论引申的强引力场中特殊的光学效应。
20世纪80年代以来,天文观测发现了许多引力透镜效应的实例,包括 爱因斯坦环 。
一些本来很难探测的非常遥远、非常暗弱的天体,幸亏引力透镜效应而进入当代天文学家的视野。
大爆炸 70万年以后,宇宙处于延续4~5亿年的 黑暗年代 ,物质大体呈均匀结构,没有任何自主发光的天体。
星光灿烂的辉煌时期始于何时?引力透镜效应的观测给出了相关信息。
被称为21世纪 两朵乌云 之一的暗物质,比所有人类已知物质的总量多4倍以上,不发出任何辐射,不可能被直观测到。
引力透镜效应作为发现宇宙暗物质的探针,在寻找暗物质确实存在的直接证据和分析暗物质的空间分布方面作出了贡献。
1引力透镜效应产生的原因引力透镜是强引力场中一种特殊的光学效应。
假设地球与一颗遥远的天体之间刚好有一个强引力场天体,三者差不多在一条直线上,强引力场天体附近的时空弯曲使远方天体的光不能沿直线到达地球,而使地球上观测到的像偏离了它原本所在的方向,其效果类似于透镜对光线的折射作用,称为引力透镜效应(图1,见彩插二)。
早在1911年爱因斯坦即提出远方恒星的光线掠过太阳表面时会发生微小的偏转,1919年5月25日英国天文学家爱丁顿率领的观测队在非洲普林西比岛通过日全食观测验证了这一结果。
这是引力透镜效应的最初概念。
产生引力透镜效应的中间天体叫做前置天体。
这一效应可能产生双重像或多重像,这些像有相同的光谱结构和谱线位移量。
特殊情况下,远方天体的像会形成环状(爱因斯坦环)。
引力透镜效应可能改变像的亮度分布,或者造成图像畸变,或者使亮度增强(图2,见彩插二)。
1泡利不相容原理具体指的是同一体系内的任意两个()不可能有完全相同的运动状态。
(1.0分)1.0?分•A、电子•B、质子•C、中子•D、原子核我的答案:A2花样滑冰运动员在冰上旋转时,哪种动作可以获得更快的转速?()(1.0分)1.0?分•A、下蹲和直立、双臂向上双腿向下并拢•B、下蹲和单足点地,其余三肢全部横向伸展•C、张开双臂和直立、双臂向上双腿向下并拢•D、张开双臂和单足点地,其余三肢全部横向伸展我的答案:A3中国古人记载的公元185年超新星爆发的文字中,有可能反映了恒星化学组成的变化的语句是()。
(1.0分)1.0?分•A、客星出南门中•B、大如半筵•C、五色喜怒•D、至后年六月消我的答案:C4太阳的寿命预计还有()亿年。
(1.0分)1.0?分•A、46•B、50•C、100•D、700我的答案:B5理论上应该出现的在各个不同波段,辐射强度分布的情况,这种分布被称为( )。
(1.0分)1.0?分•A、正太分布•B、普朗克分布•C、t分布•D、泊松分布我的答案:B6黑洞二字分别指的是()。
(1.0分)1.0?分•A、这个天体是黑色的和天体存在洞穴结构•B、这个天体是黑色的和所有的物质在视界内都往中心奇点坠落•C、任何电磁波都无法逃出这个天体和天体存在洞穴结构•D、任何电磁波都无法逃出这个天体和所有的物质在视界内都往中心奇点坠落我的答案:D7以下哪位华裔科学家对暗物质探索的贡献最大?()(1.0分)1.0?分•A、杨振宁•B、李政道•C、丁肇中•D、朱棣文我的答案:C8太阳系的6重物质界限中,没有太“大块”的天体物质的是哪一重?()(1.0分)1.0?分•A、小行星带•B、柯伊伯带•C、奥尔特云•D、太阳风的最远范围我的答案:C9暗物质的特征不包括()。
(1.0分)1.0?分•A、总量比亮物质多10倍以上•B、不发出任何辐射,但存在引力•C、质量大,寿命长,作用弱•D、主体应该是已知重粒子以外的物质我的答案:A10银河在星空中的“流域”没有涵盖哪个星座?()(1.0分)1.0?分•A、天鹅座•B、天蝎座•C、南十字座•D、狮子座我的答案:B11假如冥王星上有智慧生命,则“他们”对飞掠而过的“新视野”号做出的反应可能会是()。
《星海求知:天文学的奥秘》期末考试及答案一、单选题(题数:50,共?50.0?分)1、各种寻找系外行星的方法中,“产量”最多的是()。
A、视向速度法B、凌星法C、直接成像法D、不清楚正确答案:B?2、银河系的中心方向主要位于哪个星座?()A、天琴B、天鹰C、人马D、天蝎正确答案:C?3、开普勒探测器使用的搜寻系外行星的方法是()。
A、视向速度法B、凌星法C、直接成像法D、微透镜法正确答案:B?4、黑洞、白洞和虫洞当中,目前可以视为已经有观测证据的是()。
A、黑洞B、白洞C、虫洞D、都没有正确答案:A?5、上弦月相对于朔月的日月角距变化了()度。
A、45B、90C、180D、270正确答案:B?6、“三起源”不包括()的起源问题。
B、天体C、生命D、人类正确答案:D?7、“不同历史时期宇宙膨胀速度不同”,这里“不同历史时期”相比于现代,几乎不会考虑()时期。
A、137亿年前B、50亿年前C、10亿年前D、旧石器时代正确答案:D?8、由于岁差原因,现在的黄道春分点已经位于()星座的位置。
A、白羊B、金牛C、双鱼正确答案:C?9、以下现象,不是由太阳活动导致的是()。
A、日冕物质喷射B、极光C、黑子D、太阳周年视运动正确答案:D?10、太阳系前五大卫星当中,质量与其所属行星质量最接近的是:()A、木卫三B、月球C、土卫六D、木卫四正确答案:B?11、宇宙标准模型中,时间是宇宙创生的()秒之后开始的。
A、10^(-4)B、10^(-10)C、10^(-36)D、10^(-44)正确答案:A?12、人类目前认识到的全部的宇宙物质,占全部宇宙物质的份额接近()。
A、.05B、.25C、.5D、1正确答案:A?13、大爆炸模型在()年代正式确立为标准宇宙模型。
A、1930年代-1940年代B、1940年代-1950年代C、1970年代-1980年代D、1980年代-1990年代正确答案:C?14、以下生物组合与“动物-植物-真菌-原核生物-原生生物”的分类顺序不一致的是()。
暗物质粒子的物理性质和引力相互作用暗物质是宇宙学中一个引人注目的谜题。
虽然我们无法直接观测和探测到暗物质,但通过其引力相互作用和对宇宙结构的影响,科学家们已经积累了大量关于暗物质的证据和理论。
首先,暗物质的物理性质是什么呢?根据目前的观测结果,我们知道暗物质不与电磁辐射相互作用,因此它不会发出或吸收光线。
这就是为什么我们无法直接探测到它的原因。
然而,通过观测宇宙中的星系和星团的运动,我们可以确定暗物质必须具有质量。
这是因为只有具备一定质量的物体才能对其周围的物体施加引力。
因此,暗物质被认为是一种具备质量但没有电磁相互作用的物质。
其次,引力相互作用是暗物质的一个重要性质。
正是因为暗物质具备质量,才能通过引力相互作用影响周围的物体。
暗物质通过引力对宇宙中的可见物质产生了重要的影响。
例如,暗物质的存在解释了星系旋转曲线的异常现象。
根据牛顿的引力定律,我们预期星系中的物体应该随距离中心的增加而运动速度减小,形成一个缓和的旋转曲线。
然而观测结果显示,星系中的物体运动速度在大半径范围内保持稳定,这表明星系中存在大量的暗物质。
暗物质通过引力相互作用增加了星系中物体的运动速度,使得旋转曲线更陡峭。
类似的现象也被观测到了星系团和宇宙大尺度结构中。
因此,引力相互作用成为证实和研究暗物质的重要手段。
暗物质的粒子性质仍然是一个悬而未决的问题。
目前有一些可能的候选粒子,例如Weakly Interacting Massive Particles(微弱相互作用的大质量粒子,简称WIMPs)和Axions(轴子),但尚未有确凿的实验证据支持这些候选粒子。
这也是当前暗物质研究的重要方向之一。
关于暗物质的研究还有一些激动人心的新进展。
例如,科学家们利用宇宙微波背景辐射的观测数据,与大规模结构模拟相结合,可以推断出暗物质中各个成分的相对比例。
此外,在地下实验室中,研究人员正在努力探测暗物质粒子的直接信号。
这些实验的目标是通过探测暗物质粒子与普通物质粒子的相互作用,进一步推进对暗物质本质的认识。
“厚”此“薄”彼的银河系
谢懿
【期刊名称】《天文爱好者》
【年(卷),期】2016(000)012
【摘要】沉浸在银河淡淡的光辉之下.让人很难认识到地球其实只是这个宇宙中最大的旋涡星系之一里面极其微小的一部分。
而时至今日天文学家才开始对我们所在的这个星系有了全面的了解。
通常.我们在教科书或者书刊杂志上所看到的都是有着宏象旋涡结构的银河系正面图。
然后,为了真正了解它到底是如何形成和演化的,你需要了解唯有从侧向才能直接看到的银河系垂直结构。
【总页数】6页(P50-55)
【作者】谢懿
【作者单位】
【正文语种】中文
【中图分类】P156
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因版权原因,仅展示原文概要,查看原文内容请购买。
a r X i v :a s t r o -p h /0205281v 2 2 O c t 2002ApJ,in pressPreprint typeset using L A T E X style emulateapj v.14/09/00THE STRUCTURE AND DYNAMICS OF LUMINOUS AND DARK-MATTER IN THEEARLY-TYPE LENS GALAXY OF 0047−281AT Z=0.4851L ´e on V.E.Koopmans California Institute of Technology,TAPIR,130-33,Pasadena,CA 91125Tommaso TreuCalifornia Institute of Technology,Astronomy,105-24,Pasadena,CA 91125leon@,tt@ApJ,in pressABSTRACTWe have measured the kinematic profile of the early-type (E/S0)lens galaxy in the system 0047−281(z =0.485)with the Echelle Spectrograph and Imager (ESI)on the W.M.Keck–II Telescope,as part of the Lenses Structure and Dynamics (LSD)Survey .The central velocity dispersion is σ=229±15km s −1,and the dispersion profile is nearly flat to beyond one effective radius (R e ).No significant streaming motion is found.Surface photometry of the lens galaxy is measured from Hubble Space Telescope images.From the offset from the local Fundamental Plane (FP),we measure an evolution of the effective mass-to-light ratio of ∆log M/L B =−0.37±0.06between z =0and z =0.485,consistent with the observed evolution of field E/S0galaxies.(We assume h 65=1,Ωm =0.3and ΩΛ=0.7throughout.)Gravitational lens models provide a mass of M E =(4.06±0.20)×1011h −165M ⊙inside the Einstein radiusof R E =(8.70±0.07)h −165kpc.This allows us to break the degeneracy between velocity anisotropy and density profile,typical of dynamical models for E/S0galaxies.We find that constant M/L model,even with strongly tangential anisotropy of the stellar velocity ellipsoid,are excluded at >99.9%CL.Thetotal mass distribution inside R E can be described by a single power-law density profile,ρt ∝r −γ′,with an effective slope γ′=1.90+0.05−0.23(68%CL;±0.1systematic error).Two-component models yield an upper limit (68%CL)of γ≤1.55(1.12)on the power-law slope of the dark-matter density profile and a projected dark-matter mass fraction of 0.41(0.54)+0.15−0.05 +0.09−0.06 (68%CL)inside R E ,for Osipkov–Merritt models with anisotropy radius r i =∞(R e ).The stellar M ∗/L values derived from the FP agrees well with the maximum allowed value from the isotropic dynamical models (i.e.the “maximum-bulge solution”).The fact that both lens systems 0047−281(z =0.485)and MG2016+112(z =1.004)are well described inside their Einstein radii by a constant M ∗/L stellar mass distribution embedded in a nearly logarithmic potential –with an isotropic or a mildly radially anisotropic dispersion tensor –could indicate that E/S0galaxies underwent little structural evolution at z 1and have a close-to-isothermal total mass distribution in their inner regions.Whether this conclusion can be generalized,however,requires the analysis of more systems.We briefly discuss our results in the context of E/S0galaxy formation and cold-dark-matter simulations.Subject headings:gravitational lensing —galaxies:elliptical and lenticular,cD —galaxies:evolution—-galaxies:formation —galaxies:structure1.introductionTo understand the evolution and internal structure of luminous and dark matter in early-type galaxies (E/S0),we have started the Lenses Structure and Dynamics (LSD)Survey.From an observational point of view,the LSD Sur-vey aims at measuring –using the Keck-II Telescope –the internal (stellar)kinematics of a relatively large sample of E/S0gravitational-lens galaxies in the redshift range z =0−1(see Treu &Koopmans 2002,hereafter TK02,for a description of the survey and its scientific ratio-nale).The stellar kinematic profiles are combined with constraints from a gravitational-lensing analysis –in par-ticular the mass enclosed within the Einstein radius –in order to break degeneracies inherent to each method in-dividually.In this way,we are uniquely able to constrainthe luminous and dark mass distribution and the velocity ellipsoid of the luminous (i.e.stellar)component.Several of the main questions about E/S0galaxies that we aim to answer with the LSD Survey are:(i)What is the amount of dark matter within the inner few effective radii (R e )?(ii)Does the dark matter density profile agree with the universal profiles inferred from CDM simulations (Navarro,Frenk &White 1997,hereafter NFW;Moore et al.1998;Ghigna et al.2001)?(iii)Is there a universal to-tal (luminous plus dark-matter)density distribution that well describes the inner regions of E/S0galaxies?If so,is it isothermal,as observed in the local Universe and often assumed in lensing analyses?(iv)How does the stellar mass-to-light ratio of E/S0galaxies evolve with redshift,and does it agree with the evolution of the stellar popu-lations of field early-type galaxies as inferred from Fun-1Based on observations collected at W.M.Keck Observatory,which is operated jointly by the California Institute of Technology and the University of California,and with the NASA/ESA Hubble Space Telescope,obtained at STScI,which is operated by AURA,under NASA contract NAS5-26555.12Koopmans&Treudamental Plane(hereafter FP)measurements(Treu et al. 1999,2001a,2002,hereafter T99,T01a,T02;Kochanek et al.2000;van Dokkum et al.2001)?(v)Does the struc-ture of E/S0galaxies evolve between z=0and1,or is the evolution of the FP purely an evolution of the stellar population?(vi)Is the stellar velocity dispersion tensor isotropic or anisotropic?First results from the LSD Survey were presented in two recent papers(Koopmans&Treu2002,hereafter KT02;TK02),where we combined our measurement of the luminosity-weighted stellar velocity dispersion of the lens galaxy in MG2016+112at z=1.004with the mass en-closed by the Einstein radius as determined from gravita-tional lens models(Koopmans et al.2002).A robust con-straint was found on the slope of the total density profile of the lens galaxy,i.e.γ′=2.0±0.1±0.1(random/systematic errors)forρt∝r−γ′.In addition,we were able to deter-mine the stellar mass-to-light ratio and constrain the slope of the dark-matter halo,leading to a relatively simple self-consistent picture of the lens galaxy:an old and metal-rich stellar component embedded in a logarithmic(i.e.isother-mal)potential observed at a look-back time of∼8Gyrs –remarkably similar to many present-day E/S0galaxies. Constant M/L models were ruled out at a very high confi-dence level and a significant mass fraction(∼75%)of dark matter was shown to be present inside the Einstein ra-dius of about13.7kpc.Unfortunately,given the faintness of the galaxy at z=1,only a luminosity-weighted velocity dispersion could be obtained and only minimal constraints could be set on the anisotropy of stellar orbits.In this paper,we present Keck and HST observations, a gravitational-lens model,and a dynamical model of the lens galaxy in0047−281at z=0.485(Warren et al.1996, 1998,1999).This galaxy is bright and sufficiently ex-tended that we were able to measure a spatially resolved velocity dispersion profile,thus setting unprecedented con-straints on the orbital structure of a galaxy at a look-back time of∼5Gyrs.The paper is organized as follows.In Section2,we de-scribe archival HST observations and spectroscopic obser-vations with ESI on the Keck–II telescope.In Section3,we analyze these observations and determine the luminosity evolution of the lens galaxy with respect to the local Fun-damental Plane.In Section4,we present a gravitational lens model from which we determine the mass enclosed by the Einstein radius.In Section5,we present a model for the luminous and dark-matter distributions of the lens galaxy.In Section6,the results from the dynamical mod-els are presented.Section7summarizes and discusses the results.In the following,we assume that the Hubble constant, the matter density,and the cosmological constant are H0=65h65km s−1Mpc−1,Ωm=0.3,andΩΛ=0.7, respectively.Throughout this paper,r is the radial coor-dinate in3-D space,while R is the radial coordinate in 2-D projected space.2.observations2.1.Hubble Space Telescope ImagingWide Field and Planetary Camera2(WFPC2)images of the system are available from the HST archive,through filters F555W and F814W2.In particular,the system has been imaged for9500s in F555W on the Wide-Field Cam-era,and2700s in F814W on the PlanetaryCamera.Fig. 1.—Left:HST F555W image of0047−281.The images are designated A,B,C and D from the upper right going clockwise. Right:Same image with a smooth galaxy model subtracted.Note the almost continuous ring structure including images A,B,and C. The images were reduced using a series of iraf scripts based on the iraf package drizzle(Fruchter&Hook 2002),to align the independent pointings and perform cos-mic ray rejection.A subsampled(pixel scale0.′′05)image was produced for the F555W image.Thefinal“drizzled”image in F555W is shown in Fig.1.Note that for the red-shift of the source,z=3.595,Ly-αis redshifted to5589˚A (Warren et al.1998)and the F555W magnitude there-fore includes the bright Ly-αemission.The F814W image is significantly shallower than the F555W image and al-though adequate for measuring the structural parameters, it is not particularly useful for the lens modeling,since the multiple images are faint and their positions cannot be accurately determined.Surface photometry was performed on the F555W and F814W images as described in T99and Treu et al.(2001b; hereafter T01b).The galaxy brightness profiles are well represented by an R1/4profile,which wefit–taking the HST point spread function into account–to obtain the ef-fective radius(R e),the effective surface brightness(SB e), and the total magnitude.The relevant observational quan-tities of galaxy G in0047−281and their errors are listed in Table1.Note that errors on SB e and R e are tightly correlated and that the uncertainty on the combination log R e−0.32SB e that enters the Fundamental Plane(see Section3)is very small(∼0.015;see Kelson et al.2000; T01b;Bertin,Ciotti&del Principe2002).In the right hand panel of Fig.1we show the HST image after removal of a smooth model for the lens galaxy.Notice the nearly circular structure of the lensed image configuration around the lens galaxy.Rest frame photometric quantities listed in Table1–computed as described in T01b–are corrected for galactic extinction using E(B–V)=0.016from Schlegel,Finkbeiner &Davis(1998).2.2.Keck SpectroscopyWe observed0047−281using the Echelle Spectro-graph and Imager(ESI;Sheinis et al.2002)on the W.M.Keck–II Telescope during four consecutive nights2Obtained as part of the CASTLeS SurveyThe Structure and Dynamics of the Early-Type Lens Galaxy of0047−2813 (23–26July,2001),for a total integration time of20,700s(7x1800s+3x2700s).The seeing was good(0.′′6<FWHM<0.′′8)and three out of four nights were photometric.Be-tween each exposure,we dithered along the slit to allowfor a better removal of sky residuals in the red end of thespectrum.The slit(20′′in length)was aligned with themajor axis of the galaxy.The slit width of1.′′25yieldsan instrumental resolution of30km s−1which is adequatefor measuring the stellar velocity dispersion and removingnarrow sky emission lines.The centering of the galaxyin the slit was constantly monitored by means of the ESIviewing camera(the galaxy was bright enough to be visiblein a few seconds exposure)and we estimate the centeringperpendicular to the slit to be accurate to 0.′′1.Redshift(G)0.485±0.001F814W(mag)18.67±0.09F555W(mag)20.61±0.09SB e,F814W(mag/arcsec2)20.23±0.22SB e,F555W(mag/arcsec2)22.59±0.07R e,F814W(arcsec)0.82±0.12R e,F555W(arcsec)0.99±0.04b/a=(1−e)0.80±0.10Major axis P.A.(◦)67±5(0.0–0.2)×1.2521912(0.2–0.8)×1.2521214(0.8–1.4)×1.2520513Table2.—Kinematic data along the major axis of0047−281. The adjacent rectangular apertures are indicated.The seeing was0.′′7during the observations.Using the procedure detailed in T01b,the value in the central aperture can be corrected to standard central ve-locity dispersion ofσ=229±15km s−1within a circular aperture of radius R e/8(see also Sec.6.1).No evidence for significant streaming motions(e.g.rotation)was found, with an upper limit of50km s−1relative radial velocity between the center and the outermost aperture.3.the fundamental plane and the evolution ofstellar populationsEarly-type galaxies in the local Universe occupy approx-imately a plane in the three-dimensional space defined by the parameters effective radius(log R e),effective surface brightness(SB e)and central velocity dispersion(logσ),log R e=αlogσ+βSB e+γFP(1) known as the Fundamental Plane(hereafter FP;Dressler et al.1987;Djorgovski&Davis1987).In recent years,it has been shown that a similar cor-relation between those observables exists in clusters out to z∼0.8(e.g.van Dokkum&Franx1996;Kelson et al.1997;Bender et al.1998;Pahre1998;van Dokkum et al.1998;Jørgensen et al.1999;Ziegler et al.2001).The observed evolution of the interceptγFP of the FP with redshift is consistent with the expectations of passive evo-lution models for an old stellar population(redshift of for-mation z f 2;see e.g.van Dokkum et al.1998).No evidence for a dramatic evolution of the slopesαandβof the FP with redshift is found with the available data(see Jørgensen et al.1999,Kelson et al.2000,and T01a for discussion).The correlation is observed to be tight also in intermediate redshiftfield samples,although a faster evo-lution of the intercept is found in the highest redshiftfield samples(to z∼0.7)and interpreted as evidence for sec-ondary episodes of star formation in thefield population at z<1(T02;see also T99,T01a,Kochanek et al.2000, van Dokkum et al.2001,Trager et al.2000).Assuming that galaxy G in0047−281lies on a FP with slopes similar to those in the local Universe–and pure luminosity evolution–we can determine the offset of3developed by D.Sand and T.Treu;Sand et al.(2002),in prep.4Koopmans &Treuits effective mass-to-light ratio (M/L ∝σ210−0.4SB e /R e )with respect to the local relation,which is related to the evolution of the intercept by ∆log M/L =−0.4∆γFP /β.As the local FP in the B band we adopt the relation found by Bender et al.(1998),i.e.α=1.25,β=0.32,and γFP =−8.895−log h 50.In this way,we obtain ∆log M/L B =−0.37±0.06.The error is dominated by the observed FP parameters of galaxy G and dominates uncertainties on the local FP relation.In Fig.2we plot the evolution of the effective M/L for cluster and field E/S0galaxies as function of redshift (dashed and solid line;from T02),together with the value obtained for galaxy G (large filled square).The effective M/L evolution for galaxy G is consistent with what is observed for field galaxies,i.e.faster than for the cluster sample,possibly indicat-ing younger luminosity-weighted stellar populations (see,e.g.,T01a,T02).As described and discussed in TK02,we can use this measurement to infer the stellar mass-to-light ratio (M ∗/L B )of galaxy G assuming thatlog(M ∗/L B )z =log(M ∗/L B )0+∆log(M/L B ),(2)where the second term on the right hand side of the equa-tion is measured from the evolution of the FP,and the first term on the right hand side of the equation can be measured for local E/S0galaxies.Note that Equa-tion 2uses the non-trivial assumption that the stellar mass is a redshift-independent function of the combina-tion of observables used to define the effective mass σ2R e (for a full discussion see T02,and TK02).Using the lo-cal value of (7.3±2.1)h 65M ⊙/L B,⊙determined from data by Gerhard et al.(2001)as in TK02,we infer M ∗/L B =(3.1±1.0)h 65M ⊙/L B,⊙for galaxyG.Fig.2.—Evolution of the M/L as inferred from the evolution of the FP.The solid and dashed lines indicate linear fits to the M/L evolution for field (T02)and cluster E/S0galaxies (van Dokkum et al.2001)respectively.The large filled square at z =1.004indicates the M/L evolution of galaxy D in MG2016+112(KT02)while the large filled square at z =0.485represents galaxy G in 0047−281.4.gravitational–lens modelThe Einstein radius (R E )and mass enclosed by the Ein-stein radius,i.e.M E ≡M (<R E )are quantities required in the dynamical models that will be discussed in Sec.5.Both R E and M E are very insensitive to the assumed mass profile (see e.g.Kochanek 1991),especially for highly sym-metric cases such as 0047−281(see Fig.1).For consistency –to ensure uniform modeling throughout the LSD survey –we model the lens galaxy as a Singular Isothermal Ellip-soid (SIE;Kormann et al.1994;see also Chen,Kochanek&Hewitt 1995;Kochanek 1995;Grogin &Narayan 1996;Koopmans &Fassnacht 1999;Cohn et al.2001;Mu˜n oz,Kochanek &Keeton 2001;Rusin et al.2002).Although the assumption of a SIE mass distribution might not be accurate enough for some applications (see,e.g.,Saha 2000,Rusin &Tegmark 2001,Wucknitz 2002),we again stress that this choice of the mass profile does not signifi-cantly bias the determination of the quantities used in our analysis,i.e.M E and R E .The reason is that the image deflection angles in four-image systems like 0047−281are not only nearly the same,but also that the deflection an-gle is only a function of the enclosed mass and therefore is little affected by either the radial mass profile or the ellipticity of the lens (see §3in Kochanek 1991for a more detailed discussion).Constraints on the mass density pro-file obtained in Sec.5are therefore virtually independent of the choice of lens mass model.Image∆x (′′)∆y (′′)δ(x,y )(mas)The Structure and Dynamics of the Early-Type Lens Galaxy of 0047−2815surface brightness distribution (Table 1)and the presence of an external shear is allowed for.Hence,there are six free parameters (i.e.the ellipticity and velocity dispersion of the lens-galaxy mass distribution,the source position,and the external shear),eight constraints (i.e.the four image positions)and consequently two degrees of freedom.The velocity dispersion of the SIE mass model is defined such that the mass enclosed by the critical curve is equal to that inside the Einstein radius of a Singular Isothermal Sphere with the same velocity dispersion (Kormann et al.1994).Fig.4.—Velocity dispersion profile of 0047−281along the majoraxis.The box height indicates the 68%measurement error,whereas the box width indicates the spectroscopic aperture (times the slit width 1.′′25).The open squares are the corresponding values for an isotropic constant M/L model,whereas the open stars are for a model with 10%lower M E (twice its error)and 10%higher R e (both of which lower σ)with r i =∞.The open circles indicate the isotropic Hernquist luminous component embedded in a total mass distribution with γ′=1.90.See Section 6for details.The best solution for a single SIE mass distribution yields σSIE =253km s −1for the lens galaxy,whereas the required external shear is 0.13.The χ2is rather high,306for two degrees of freedom.It is possible to device more elaborate models (for example with a dwarf companion)that fit the observational constraints much better.How-ever –as mentioned before –the mass enclosed by the Einstein radius is very insensitive to the precise lensing model.As an illustration of the uncertainty related to the mass modeling we considered including a dwarf companion galaxy with σSIE ∼60km s −1.Although the fit is greatly improved (χ2=0because there are more free parameters than constraints),the velocity dispersion of the primary lens changes by only −4km s −1.We will therefore not elaborate further on the details of the lens model –which is not the intention of this paper –and use the results from SIE mass model in the rest of the analysis.More detailed lens models are being constructed based on the structure in the lensed arcs (R.Webster,private communication).We note that σSIE is close to the central stellar velocity dispersion (Table 1).However,we emphasize that σSIE is a model-dependent expression of the well-determined total enclosed mass,while the central stellar velocity dis-persion depends on the precise total mass profile,on the luminous mass profile,and on the dynamical state of the luminous component.Hence,the two quantities do not have to agree in principle.Their agreement is rather anindication of a regular behavior in the physical properties of early-type galaxies,as discussed in Sections 5,6and 7(see also Kochanek 1994and Kochanek et al.2000).The adopted SIE velocity dispersion corresponds to acircular Einstein radius of R E =(8.70±0.07)h −165kpc (i.e.θE =1.′′34±0.′′01)and an enclosed mass of M E =4.06×1011h −165M ⊙.The errors on R E and M E are cor-related (both depend on σSIE ):for fixed R E one finds that δM E /M E =2(δσSIE /σSIE ).This error corresponds to about 3%for δσ=4km s −1,i.e.the difference be-tween the model with and without an additional compan-ion galaxy,which we adopt as systematic error (the ran-dom error on σSIE is a negligible 0.5%).By adopting a wide range of mass profiles and/or ellipticities the enclosed mass changes by 4%for symmetric four-image systems like 0047−281(e.g.Kochanek 1991).Hence,adding the two contributions in quadrature,the total error becomes5%on M E inside a radius of R E ≡8.70h −165kpc.5.dynamical modelFollowing TK02,we model the galaxy mass distribution as a superposition of two spherical components,one for the luminous stellar matter and one for the dark-matter halo 4.The luminous mass distribution is described by a Hernquist (1990)modelρL (r )=M ∗r ∗(r/r b )γ(1+(r/r b )2)(3−γ)/2(4)which closely describes a NFW profile for γ=1,and has the typical asymptotic behavior at large radii found from numerical simulations of dark matter halos ∝r −3(e.g.Ghigna et al.2000).See TK02for further discussion of this mass profile and dynamical model.According to the CDM simulations given in Bullock et al.(2001),a galaxy with the virial mass of galaxy G at z =0.485has r b ≈50kpc ≫R e ∼R E .Hence,in the light of a comparison with CDM models,we can safely assume that the dark matter profile in the region of in-terest (i.e.inside ∼R E )is well described by a power-law ρd ∝r −γ.Throughout this study,we will set r b =50kpc (effectively equal to r b =∞).The effects of changing r b are discussed in TK02.In addition,we assume an Osipkov-Merritt (Osipkov 1979;Merritt 1985a,b)parametrization of the anisotropy βof the luminous mass distributionβ(r )=1−σ2θr 2+r 2i,(5)where σθand σr are the tangential and radial componentof the velocity dispersion and r i is called the anisotropy4Spherical dynamical models provide an adequate approximate description for computing kinematic quantities of E/S0galaxies with axis ratio b/a ∼0.8like 0047-281(e.g.Saglia,Bertin &Stiavelli 1992;Kronawitter et al.2000),even though clearly they are not appropriate for the lensing analysis,since,e.g.,they do not produce quadruply lensed images.6Koopmans&Treuradius.Note thatβ>0by definition,not allowing tan-gentially anisotropic models.A brief discussion of tangen-tially anisotropic models with negative constant values of βis given in Sec.6.2.As a further caveat,note that at infinite radii,Osipkov-Merrit models become completely radial.Although this behavior is not commonly found within the inner regions of E/S0probed by observations (e.g.Gerhard et al.2001;but see van Albada1982and Bertin&Stiavelli1993for theoretical grounds),it has lit-tle impact in the case considered here,since the pressure tensor only becomes significantly radial well outside the Einstein Radius and in projection is significantly down-weighted by the rapidly falling luminosity–density profile. The line-of-sight velocity dispersion is obtained solving the three dimensional spherical Jeans equation(e.g.Bin-ney&Tremaine1987Eq.4-30)for the luminous compo-nent in the total gravitational potential and computing the luminosity-weighted average along the line of sight(Bin-ney&Tremaine1987;Eq.4-60;see also,e.g.Ciotti,Lan-zoni&Renzini1996).We correct for the average seeing of0.7′′,during the observations,and average the velocity dispersion–weighted by the surface brightness–inside the appropriate rectangular apertures.For completeness, we rescale the apertures(Table2)by0.9and1.1in the directions of the major and minor axes,respectively,such that their projection on the axisymmetric model is equiv-alent to their projection on an elliptical galaxy with an axial ratio of0.8,even though this has minimal effects on the model velocity dispersions(<1%),much smaller than the observational errors.The uncertainties on seeing, aperture size,and galaxy centering are taken into account as systematic errors in the following discussion.6.luminous and dark matter in0047−281 The unknown parameters of our dynamical model are M∗,γ,r i andρd,0(we note again that r∗=R e/1.8153and r b=50kpc).We can eliminate one of these parameters using M E,the mass inside the Einstein radius,which is the most accurately known constraint on the lens mass model. We choose to eliminateρd,0.In addition,we transform M∗into the stellar mass-to-light ratio M∗/L B,fixing the model luminosity exactly to the value1.2×1011h−265L B,⊙. Hence,values of M∗/L B that we derive from the dynami-cal model,bears an additional uncertainty of11%,i.e.the observational error on L B,whereas M∗,which is used in the model calculation,does not have this error.We use the average R e=(5.52±0.55)h−165kpc of the rest-frame V–and B–band values.For any given set{M∗/L B,γ}the dynamical model is completely determined and the luminosity-weighted veloc-ity dispersions for each of the three apertures(Tab.2) can be computed.The likelihood is determined assuming Gaussian error distributions and the confidence contours using the likelihood ratio statistic5.6.1.Power-Law ModelsBefore studying the luminous and dark-matter profiles individually,we determine the effective slope(γ′)of the total(luminous plus dark)matter density profile(ρt)in-side the Einstein radius.We emphasize that an effective slope ofγ′does not imply that the density profile follows ρt∝r−γ′exactly,but only effectively.For MG2016+112(TK02)we measured an effective slopeγ′=2.0±0.1±0.1(random and systematic er-rors),assumingρt∝r−γ′.Based on the data in Warren et al.(1998)and Kochanek et al.(2000),we found a similar effective slope for0047−281.However,the errors were rel-atively large due to a lack of an extended kinematic profile and the large uncertainty on the velocity dispersion given by Warren et al.(1998).With the data presented here we can perform a more accurate measurement,and set con-straints on the anisotropy of the velocity ellipsoid.In Fig.5(c),we show the likelihood contours ofγ′ver-sus the anisotropy radius r i,based on our extended kine-matic profile of0047−281.Three main conclusions can be drawn:(i)for a spherical isotropic stellar distribution function(r i→∞)γ′=1.90±0.05(68%CL)(see also Fig.4);(ii)a lower limit of r i/R e 0.7(68%CL)can be set,implying that the velocity distribution function is isotropic in the inner regions of the galaxy;(iii)indepen-dent of r i,onefindsγ′=1.90+0.05−0.23(68%CL).To assess systematic errors onγ′,we varied M E and R e by the total uncertainties±5%and±10%,respectively. The value ofγ′,required tofit the data,changes by±0.05 and±0.03,respectively.Other potential sources of errors, such as seeing,aperture corrections,aperture offsets,etc., were found to be negligible.We add both contributions and we conservatively round up to a total systematic er-ror of±0.1,to account for all potential minor sources of error.Although the outer region of galaxy G is wellfit by a Hernquist(1990)model,the inner region withρL(r)∝r−1 is less constrained due to thefinite resolution of the HST images.We therefore examined power-law models with steeper inner luminosity density profiles,ρL(r)∝r−2, using the model from Jaffe(1983).For both r i=∞and r i=R e,wefind that the stellar velocity disper-sions change by≤6km s−1.In general,Jaffe models give slightly lower velocity dispersions for afixed value ofγ′and the best-fit models therefore yield slightly higher val-ues ofγ′(few hundredths)compared with the Hernquist models.However,the differences are not significant,given the errors on dispersion profile,and therefore we conclude that our results are insensitive to the precise shape of the inner luminosity density profile.For completeness,we note that our model withγ′= 1.90results in a central stellar velocity dispersion of σ=221km s−1inside R e/8,in excellent agreement with the empirically derived value ofσ=229±15km s−1in Sec.2.2,confirming the self-consistency of our models.In conclusion,the total mass distribution of galaxy G is well-matched by a single power-law density profile,that is isothermal(i.e.ρt∝r−2)to within∼5%,and the velocity ellipsoid of the luminous component is isotropic at least inside∼70%of the effective radius.Note that this limit is generally consistent with the limits set by other phys-ical considerations.In fact,strongly radial orbits would result in radial instability(e.g.Merritt&Aguilar19855Note that the likelihood ratio statistic is distributed as aχ2only asymptotically,hence the interpretation of the likelihood ratio contours as confidence contours is an approximation.However,because the confidence contours(i.e.Fig.5)on which we base our results only mildly deviate from true ellipses–i.e.the limiting case for large numbers of constraints–,this approximation should work well.。
反德西特空间中黑洞热力学的研究黑洞热力学一直以来都是很热门的主题。
另外也有很多涉及黑洞热力学的相关领域,例如黑洞的准正规模式,我们可以用它来探测黑洞的相变,还有弱宇宙监督假设,其被认为是黑洞热力学的基础。
第一章,我们主要介绍了黑洞热力学的历史,比如黑洞热力学四定律。
由于AdS/CFT对应,关于黑洞热力学的研究拓展到AdS黑洞,其中将宇宙学常数解释为热力学压强。
后面的研究表明,AdS黑洞拥有更多有趣的相结构,例如重入相变和三相点。
最后,我们也讨论了黑洞热机的概念。
第二章,我们采取了另一种宇宙学常数的解释,即将它当成规范场理论中的色数,并在黑洞热力学中引入化学势的概念。
我们发现一个五维的带电AdS黑洞中存在一个VdW型的小/大黑洞相变。
有趣的是,结果表明相变对于大色数的情况才能发生,对于小色数则不行。
在某种程度上,这表明带电AdS黑洞系统的相互作用是随着色数而增加的。
接着我们得到了共存曲线和相图,并且研究也表明,黑洞相变的信息可以从热容中得到。
第三章,我们专注于黑洞的准正规模式,其对应于一个黑洞周围的动力学涨落。
我们讨论了主方程,边界条件和打靶法。
其中,我们正是选择用打靶法来求解无质量标量场的准正规频率。
然后我们研究了洛伦兹对称性破缺的有质量引力中的带电黑洞的相变信息能否通过动力学的准正规模式行为反映出来。
有两种方法来探测相变:i)在<sub>4</sub>)-图中准正规频率的斜率符号的改变。
ii)在等压或等温过程中,准正规频率的虚部的行为。
第四章,我们将主题转到弱宇宙监督假设(WCCC),其正是黑洞热力学的基础。
弱宇宙监督假设表明,裸奇点不能够被一个远处的观者所看到,这意味着,裸奇点总是被隐藏在黑洞视界面以内。
在忽略辐射效应后,我们运用点粒子吸收的过程来研究其破坏Kerr-MOG黑洞的可能性。
我们发现,对于极端和近极端黑洞而言,在上下能量边界间总是存在一个能量间隙,这表明,一些能量合适的粒子是能够导致弱宇宙监督假设的违背。
2016 年北京大学“本科生科研训练”资助项目名单 2016-5-20院 系资助项目 名称学号姓名性 院系 指导 别 教师研究题目北京市创新 计划 1400010694李正一男数学董彬非线性降维及应用北京市创新 计划1400011051 1400010623刘子不 陈博涵男 男数学 数学董彬基于稀疏逼近的流形学习及其在图像处理 中的应用北京市创新 计划1400010713 1400010736 1400010626陈喆 李冠淳 姚嘉豪男 男 男数学 数学 数学 张平文 雾霾的计算与预测北京市创新 计划1400010687 1400010702房正阳 胡晟男 男数学 数学董彬稀疏逼近在核磁图像重建中的应用数 学 学 院北京市创新 计划 1400010611赵梓文男数学范后宏K-理论及其应用北京市创新 计划1400010727 1400010726刘育烜 于鹏男 男数学 数学吴岚股票市场动态相关性实证分析北京市创新 计划 1400010734张子筠女数学张平文液晶中加入不对称胶体粒子的数值模拟国家创新训 练项目 1400012129严煜凌男数学贾金柱L1/2 惩罚回归方法中系数的相合性国家创新训 练项目 1400010605陈成男数学赵玉凤不变量理论在李理论的应用1 / 46国家创新训 练项目 1400010653张钺男数学范后宏广义上同调理论及其应用国家创新训 练项目1400010693 1400010628 1400010700唐敦 包诚杨 熊博远男 女 男数学 数学 数学 方博汉 环簇上的一些镜对称问题国家创新训 练项目1400010696 1400012610姜杰东 吕世极男 男数学 数学许晨阳奇点的稳定性国家创新训 练项目1400010719 1400010656 1400017676郭润晨 蔡晓榕 白沅鹭男 女 女数学 数学 元培 杨静平汽车贷款资产证券化理论及中国市场的实 证研究国家创新训 练项目 1400010601丁允梓男数学张平文液晶点缺陷稳定轴对称解的研究䇹政基金1400017666 1400012933刘波 姜家隆男 男元培 元培葛颢生物代谢网络中的热力学约束䇹政基金1400013701李文远男数学范辉军辛流形中的拉格朗日子流形的几何校长基金1400010714刘定鸿男数学马翔Lorentz 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1400011005 1400011087 1400011008 沈祎恒 张钰 姚雪松 男 男 男 工学 工学 周欢萍 低成本、高效率的钙钛矿太阳能电池开发 及性能研究3 / 46钟夏校际科 研基金1400011022 1400011108周金辉 李培豪女 男工学 郭少军 工学基于三维碳-过渡金属复合材料的高性能 钠离子电池研究华宝基金1400011037柯旭瑜女工学许晓云基于大数据的汽车后市场服务——OBD 数据挖掘及智慧配送服务华宝基金1400011075丁明谦男工学王勇关于非完整动力学及 vakonom 动力学的 一些探究毛玉刚基金1400011014岳壮男工学杨越面向航空煤油替代燃料的燃烧数值模拟毛玉刚基金1400011068王英健男工学莫凡洋质子响应过渡金属配合物的合成及在氢气 储存利用中的应用䇹政基金1300018904丁瀚男工学杨越基于涡面场演化的涡重联机理研究䇹政基金1400011074刘向阳男工学于海峰聚酰亚胺基与聚合物双层膜的光机械性能 研究校长基金1400011020熊睿男工学莫凡洋质子响应过渡金属配合物的合成及在小分 子惰性化学键活化中的应用校长基金1400011103孙北奇男工学莫凡洋温室气体二氧化碳的再生利用——二氧化 碳氢化制备甲醇校长基金1400011040黄翰鑫男工学郭少军基于杂原子掺杂碳纳米材料-铜基纳米晶 复合材料的二氧化碳转换催化剂研究校长基金1400011760 1400011708彭超 焦浩洋男 男化学 周欢萍 化学 钙钛矿材料及太阳能电池的稳定性研究校长基金1400012220王宇初男物理陈正爆轰波传播特性与快速火焰向爆轰波转化 机理校长基金1400012613车元孟男地空卢海龙加拿大 Cascadia 海域与海底浅表层天然 气水合物共存的自生矿物研究物北京市创新1400011326陆跃辉男物理刘雄军第二类 Weyl 半金属中的超导性质4 / 46理 学 院计划北京市创新 计划1400011352 1400011323龙卓青 傅杨物理 男 物理 许甫荣 核天体元素合成中碳的重要性北京市创新 计划 1400011363曾俊邦男物理李源汞系铜基高温超导单晶制备和散射谱研究北京市创新 计划 1400011378潘博洋男物理高家红脑血流灌注和脑氧代谢功能核磁共振成像 的定量研究北京市创新 计划 1400011399罗杨程男物理胡永云 杨军红矮星周围类地行星大气成分的数值模拟北京市创新 计划 1400011406韩兆宇男物理穆良柱量子纠缠熵、纠缠谱在凝聚态物理中的应 用北京市创新 计划 1400011453陈文杰男物理彭良友太赫兹光源与里德堡原子的相互作用动力 学研究北京市创新 计划 1400011459任阳泽男物理林金泰国际贸易对空气质量、气候和生态系统的 影响北京市创新 计划 1400011332李兆涵男物理曹庆宏Higgs 稀有衰变与新物理北京市创新 计划1400011351 1400012603喻佳 黄佳旺男 男物理 廖志敏 物理应力对 Dirac 半金属 Cd3As2 纳米线物性 的调制北京市创新 计划 1400011309王宇晗男物理肖云峰变形腔之间的长距离耦合国家创新训 练项目 1400011311戴嘉为男物理王健新二维材料的拓扑性质研究国家创新训 练项目 1400011325Ryuichi白岸斯男物理Magnetic properties of Kitaev materials in Shindo iridates u5 / 46国家创新训 练项目 1400011327Richar张昊男物理d GrijsdeNGC1783 等球状星团的星族及宽主序转 折的研究国家创新训 练项目 1400011330梁致源男物理胡小永微纳全光调制器研究国家创新训 练项目 1400011336王天也男物理陈剑豪黑磷场效应管的量子运输测量国家创新训 练项目 1400011349吴天玮男物理刘开辉高压调控下二维材料层间相互作用和性质国家创新训 练项目 1400011355于天旻男物理陈斌引力的大 N 展开国家创新训 练项目 1400011395王希睿女物理贾爽助熔剂法生长亚稳态化合物单晶国家创新训 练项目1400011413 1400011315孙彰昊 李嘉宇男 男物理 刘雄军 物理3DTopologicalSuperconductorandTopological Insulator in New Materials国家创新训 练项目 1400011446王国庆男物理李源钌基关联电子材料的制备和谱学研究国家创新训 练项目 1400011454沈学简男物理刘富坤三个或多个超大质量黑洞的潮汐瓦解事件 特征的研究国家创新训 练项目 1400011455王劼文男物理彭良友抛物坐标系中氢原子与强激光场相互作用 的数值模拟国家创新训 练项目 1400011610李智慧男物理何子山The Gas Content of Nearby Galaxies国家创新训 练项目 1400017636祝苡钦男元培古英表面等离激元光学和量子光学交叉领域理 论研究国家创新训1400017639陈一潇男元培徐莉梅水的特性研究6 / 46练项目国家创新训 练项目 1400017686李向荣男元培林峰银纳米线中表面等离激元的传播研究林金泰 华宝基金 1400011337 王子维 男 物理 刘征宇 华北雾霾与天气的关系华宝基金1400011371袁智扬男物理方哲宇等离激元近场光学及漏辐射成像研究华宝基金1400011372汪前男物理张熙博超冷原子实验中的电学与光学仪器的搭建华宝基金1400011432张湛伯男物理东苏勃利用 LAMOST 和 Kepler 数据搜寻双星周 围的系外行星华宝基金1400011456刘至远男物理李新征多维体系量子隧穿半经典模拟方法探究䇹政基金1400011365李瑞鹏男物理方哲宇二维材料等离激元手性结构研究䇹政基金1400011428娄媛女物理李方廷细胞内的非平衡态效应Richar䇹政基金1400011603姚雨含女物理Light-curve and spectral characterization of d Grijs de Mira stars in the KISO-GP survey䇹政基金1400011612 1400011334姜旭 王雯男 女物理 穆良柱 物理 量子秘钥分配(QKD)协议的优化与改良毛玉刚基金1300013529郑宇凡男物理陈斌引力的全息性研究毛玉刚基金1400011301陈偲涵男物理刘开辉新型二维原子层材料的纳米光谱学研究Effects of complex mass distribution of 毛玉刚基金 1400011316 戴必玮 男 物理 范祖辉 dark matter halos on weak lensing peak statistics毛玉刚基金1400011370朱哲毅男物理林熙3ω 法测热导率系统的改进7 / 46校长基金1300012140王新羿男物理李奇特3D 打印核实验探测阵列研究校长基金1400011034张哲豪男物理陈斌引力的大 N 展开校长基金1400011090相成男物理贾爽外尔半金属中的反常霍尔效应校长基金1400011307顾羽中男物理肖云峰光学微腔中的混沌辅助隧穿效应校长基金1400011314郭阳观男物理刘雄军基于 Majorana 费米子的拓扑量子计算校长基金1400011319 1400011329陈兴炎 周洲男 男物理 许甫荣 物理 弱束缚强关联量子系统校长基金1400011324袁琪男物理史俊杰单原子层超薄量子阱的受限电子态及二维 LED 发光机理研究校长基金1400011338何任川男物理肖池阶等离子体实验研究校长基金1400011348陈哲峰男物理陈剑豪低维器件制备与原子量子输运测量校长基金1400011354辜宸阳男物理杨根DNA 的损伤和修复校长基金1400011357王爽男物理曲波新型太阳能电池研究校长基金1400011359陈成男物理刘开辉激光诱导超快电子场发射校长基金1400011364许玮璇女物理胡永云南半球平流层变暖现象及其成因校长基金1400011366 1400061307蔡子东 胡义涵男 男物理 方哲宇 物理 新型二维材料等离激元光电器件研究校长基金1400011367凡达男物理林金泰利用模型计算大气及贸易导致的污染输送 问题校长基金1400011368孔浩男物理林金泰大气污染的物化模型发展与应用校长基金1400011373黄代强男物理肖立新杂化钙钛矿太阳能电池的特性及其湿度稳8 / 46定性研究校长基金1400011383俞文锦男物理傅宗玫北美地面 PM2.5 浓度对气候年际及年代际 变化的敏感性校长基金1400011385余泓烨男物理吴飙量子算法校长基金1400011388郭伟轩男物理张熙博建造高灵敏度的光电探测器并探索其在超 冷原子与光学实验中的应用校长基金1400011392 1400011623雷孟铼 陆家明男 男物理 陈志坚 物理 可调节透光的智能光伏器件校长基金1400011396黎晨远女物理李源低维自旋材料的谱学测量和理论分析校长基金1400011397孙金钊男物理李源铁基超导体材料的制备和谱学研究校长基金1400011403程舒羽男物理贾爽利用超临界流体反应制备新材料单晶校长基金1400011404陕思宇男物理李婧ENSO 对中高纬地区空气质量的影响校长基金1400011407童心言女物理冒亚军BESIII 实验非常规介子态研究校长基金1400011414方正男物理廖志敏拓扑材料的制备及特性研究校长基金1400011415王锦天男物理王健二维材料的制备与物性校长基金1400011417李博婷女物理鲁向阳x 射线与等离体子相互作用校长基金1400011418李佳明男物理高原加速器液态锂靶束流与液面相互作用模拟校长基金1400011419王军霞女物理肖云峰回音壁模式谐振腔传感的新机制研究校长基金1400011420汪嵩博男物理刘雄军Exotic Topological Phase in Synthetic High Dimension校长基金1400011431刘宇杰男物理张焱Cu2Sb 结构二元和三元材料的单晶合成与 研究9 / 46校长基金1400011438张思源男物理林金泰国际贸易对污染排放转移的影响校长基金1400011439杨光男物理曲波新型太阳能电池研究校长基金1400011440刘秋实男物理何琼毅多体量子纠缠的度量与分类校长基金1400011442司鑫宇女物理贾爽Heusler 金属的单晶制备和霍尔效应研究校长基金1400011445相腾男物理王大勇phi 介子的不可见衰变研究校长基金1400011447王政国男物理张焱原位可控碱金属蒸发源及超高真空传样系 统的设计与搭建校长基金1400011449 1400011626朱楠 司懿东方女 女物理 胡永云 物理 北极海冰融化和北半球中纬度寒潮校长基金1400011451王李鹏男物理方哲宇金属纳米天线研究校长基金1400011452王子鹏男物理彭良友OAM 光场的产生以及它与原子的相互作 用研究校长基金1400011463赵雅歌男物理陈建军芯片内表面等离激元传感器件研究校长基金1400011465曹睿枭男物理彭良友FEM-DVR 空间离散框架下含时薛定谔方 程传播的数值稳定性研究校长基金1400011466韩霄男物理曲波新型太阳能电池研究校长基金1400011468江嘉杰男物理王宏利具有温度补偿性的适应性生物网络设计校长基金1400011604何子麒男物理吴学兵利用宽波段时变数据开展类星体测光反响 映射研究校长基金1400011606李阮存男物理刘玉鑫脉冲星 glitch 现象的 QCD 相变机制研究校长基金1400011613孙凤梧男物理江林华搜寻和证认 UDS 深场中红移 3.1 的发射线 星系10 / 46。
arXiv:astro-ph/0306515v2 13 Jan 2004DraftversionFebruary2,2008PreprinttypesetusingLATEXstyleemulateapjv.14/09/00
PROPERTIESOFGALAXYDARKMATTERHALOSFROMWEAKLENSINGHenkHoekstra1,2,3,H.K.C.Yee2,3,andMichaelD.Gladders3,4DraftversionFebruary2,2008
ABSTRACTWepresenttheresultsofastudyofweaklensingbygalaxiesbasedon45.5deg2ofRCbandimagingdatafromtheRed-SequenceClusterSurvey(RCS).Wedefineasampleoflenseswith19.5andasampleofbackgroundgalaxieswith21.5Wepresentthefirstweaklensingdetectionoftheflatteningofgalaxydarkmatterhalos.Weuseasimplemodelinwhichtheellipticityofthehaloisftimestheobservedellipticityofthelens.Wefindabestfitvalueoff=0.77+0.18−0.21,suggestingthatthedarkmatterhalosaresomewhatrounderthanthelightdistribution.Thefactthatwedetectasignificantflatteningimpliesthatthehalosarewellalignedwiththelightdistribution.Giventheaverageellipticityofthelenses,thisimpliesahaloellipticityofehalo=0.33+0.07−0.09,infairagreementwithresultsfromnumericalsimulationsofCDM.Wenotethatthisresultisformallyalowerlimittotheflattening,sincethemeasurementsimplyalargerflatteningifthehalosarenotalignedwiththelightdistribution.Alternativetheoriesofgravity(withoutdarkmatter)predictanisotropiclensingsignal,whichisexcludedwith99.5%confidence.Hence,ourresultsprovidestrongsupportfortheexistenceofdarkmatter.Wealsostudytheaveragemassprofilearoundthelenses,usingamaximumlikelihoodanalysis.Weconsidertwomodelsforthehalomassprofile:atruncatedisothermalsphere(TIS)andanNFWprofile.Weadoptobservationallymotivatedscalingrelationsbetweenthelensluminosityandthevelocitydispersionandtheextentofthehalo.TheTISmodelyieldsabestfitvelocitydispersionofσ=136±5±3km/s(allerrorsare68%confidencelimits;thefirsterrorbarindicatesthestatisticaluncertainty,whereastheseconderrorbarindicatesthesystematicerror)andatruncationradiuss=185+30−28h−1kpcforagalaxywithafiducialluminosityofLB=1010h−2LB⊙(undertheassumptionthattheluminositydoesnotevolvewithredshift).Alternatively,thebestfitNFWmodelyieldsamassM200=(8.4±0.7±0.4)×1011h−1M⊙andascaleradiusrs=16.2+3.6−2.9h−1kpc.Thisvalueforthescaleradiusisinexcellentagreementwithpredictionsfromnumericalsimulationsforahaloofthismass.
Subjectheadings:cosmology:observations−darkmatter−gravitationallensing−galaxies:haloes
1.introductionTheexistenceofmassivedarkmatterhalosaroundgalaxiesiswidelyaccepted,basedondifferentlinesofev-idence,suchasflatrotationcurvesofspiralgalaxies(e.g.,VanAlbada&Sancisi1986)andstronglensingsystems(e.g.,Keeton,Kochanek&Falco1998).However,rela-tivelylittleisknownaboutthepropertiesofdarkmatterhalos.Stronglensingonlyprobesthegravitationalpoten-tialonsmall(projected)scales,whereasthelackofvisi-bletracersatlargeradiihamperdynamicalmethods.Todate,onlysatellitegalaxieshaveprovidedsomeinforma-tion(e.g.,Zaritsky&White1994;McKayetal.2002;Pradaetal.2003).Apromisingapproachtostudythegalaxydarkmatterhalosisweakgravitationallensing.Thetidalgravitationalfieldofthedarkmatterhalointroducessmallcoherentdis-tortionsintheimagesofdistantbackgroundgalaxies.Theweaklensingsignalcanbemeasuredouttolargeprojecteddistancesfromthelens,andhenceprovidesaunique
1CITA,UniversityofToronto,Toronto,OntarioM5S3H8,Canada
2DepartmentofAstronomy,UniversityofToronto,Toronto,Ontario
M5S3H8,Canada3VisitingAstronomer,Canada-France-HawaiiTelescope,whichis
operatedbytheNationalResearchCouncilofCanada,LeCentreNationaldeRechercheScientifique,andtheUniversityofHawaii4ObservatoriesoftheCarnegieInstitutionofWashington,813Santa
BarbaraStreet,Pasadena,California91101
probeofthegravitationalpotentialonlargescales.Theapplicationsofthisapproacharenumerous:onecaninfermassesofgalaxiesandcomparetheresultstotheirluminosities(e.g.,McKayetal.2001;Wilsonetal.2001),oronecanattempttoconstrainthehalomasspro-file(e.g.,Brainerdetal.1996;Hudsonetal.1998;Fischeretal.2000;Hoekstraetal.2003).Also,weaklensingcanbeusedtoconstraintheshapesofhalosbymeasuringtheazimuthalvariationofthelensingsignal.Unfortunately,onecanonlystudyensembleaveragedproperties,becausetheweaklensingsignalinducedbyanindividualgalaxyistoolowtobedetected.Asuccessfulmeasurementofthelensingsignalrequireslargesamplesofbothlensesandbackgroundgalaxies.ThefirstattempttodetectthelensingsignalbygalaxieswasmadebyTysonetal.(1984)usingphotographicplates.IttookmorethanadecadeandCCDcamerasbeforethefirstdetectionswerereported(Brainerdetal.1996;Grif-fithsetal.1996;Dell’Antonio&Tyson1996;Hudsonetal.1998).Theseearlyresultswerelimitedbythesmallareascoveredbytheobservations.Theaccuracywithwhichthegalaxy-galaxylensingsig-nalcanbemeasureddependsontheareaofskythatisobserved,andontheavailabitityofredshiftsforthelenses(asitallowsforaproperscalingofthelensingsignal).PhotometricredshiftswereusedbyHudsonetal.(1998)toscalethelensingsignalofgalaxiesintheHubbleDeep